Heightmap format?

In my current project I'm using a height map for an artificial potential field. From this height map I calculate a normal at an arbitrary point (average of the surrounding 8) to get a force vector.

My question is: What is the optimal format for my height map?
I'm currently thinking just an array of floats.
I need at least 16 bits of precision for height.
I want something easily saved and edited, perhaps in a graphics app like photoshop.
Right now, I'm using it purely for calculation and not display; but if possible I'd like to leverage any kind of acceleration I can out of OpenGL.
*note: I don't need to convert the whole map to a normal map, just arbitrary points, so it's not too CPU intensive (I hope).